It's difficult to find a way to refund this money without it appearing to auditors as money laundering.
Look at what it is on the surface. You'd take line item budget money from schools, write a check to an entity for entry fees, then two months later turn it around and deposit a refund check to .. the activity account?
That's illegal. You can't put budget money into your activity account, full stop. You also can't refund into a line item - to say nothing of that line item money would be GONE next school year, and you'd get nothing back anyway!
What will probably happen is that these entry fees are "held" and anyone who has already paid THIS year's UIL fees (and not gone to UIL) will have their fees paid for next year's UIL already.
If you're paying UIL fees out of activity, I bet you could talk your region exec sec into a refund - but the question becomes "why are you doing this?"